Identifier
Mp00015:
Binary trees
—to ordered tree: right child = right brother⟶
Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Images
=>
Cc0010;cc-rep-0Cc0021;cc-rep-1Cc0005;cc-rep-2
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[.,[[[[.,.],.],[.,[.,.]]],.]]=>[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[.,[[[[[[.,.],.],.],.],.],.]]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
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[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
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[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
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[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
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[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
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[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
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[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
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[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
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[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
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[[.,[.,[[[.,.],[.,.]],.]]],.]=>[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
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[[.,[.,[[[[.,.],.],.],.]]],.]=>[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
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[[.,[[.,.],[[.,[.,.]],.]]],.]=>[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
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[[.,[[.,[.,.]],[[.,.],.]]],.]=>[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
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[[.,[[[.,.],.],[[.,.],.]]],.]=>[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
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[[.,[[[.,.],[.,.]],[.,.]]],.]=>[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
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[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
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[[.,[[[.,[[.,.],.]],.],.]],.]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
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[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
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[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[.,.],[[[[.,.],.],.],.]],.]=>[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
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[[[.,[.,.]],[[[.,.],.],.]],.]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
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[[[[.,.],.],[[.,[.,.]],.]],.]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],[[[.,.],.],.]],.]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
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[[[.,[[.,.],.]],[[.,.],.]],.]=>[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
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[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
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[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
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[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
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[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
Map
to ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
- if $x$ is the left child of $y$, $x$ becomes the first child of $y$.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path is the depth of the tree.
This sends the maximal height of the Dyck path is the depth of the tree.
searching the database
Sorry, this map was not found in the database.